Session 1: Two-Dimensional Shapes – Definition, Types and Interactives

In nature, we can observe beautiful geometrical patterns and shapes. A large part of the natural world is geometric. The hexagon is a polygon with six sides and is the most common geometric shape observed in nature. Snowflakes, beehives, and insects’ compound eyes are all made up of hexagons. Why is this? Honeycombs require less wax to be constructed, can be tightly packed, and withstand compression if the grids used to build them are hexagonal. Hexagonal packing best fills a plane with equal size units leaving no wasted space, making it frequently occur in nature. 

Natural shapes like the spiral of snails, the concentric rings in tree trunks, the bodies of starfish and even spider webs display intricate geometric designs. Hence, it is important to understand the different 2D shapes and their properties.

What are Two-Dimensional Shapes or Plane Figures?

A plane figure has a dimension of two. It can be compared to a line segment because it has a specific maximum length and width but no height.

Length and width are the dimensions of a two-dimensional figure. In short, we call two-dimensional figures 2-D figures. 

Two-Dimensional Shapes: Polygons

A two-dimensional shape bounded by a number of straight lines is called a polygon.

Types of Polygons

A polygon is usually classified by its number of sides, as shown below.

Number of Sides	Name of Polygon	Shapes
3	Triangle
4	Quadrilateral
5	Pentagon
6	Hexagon
7	Heptagon
8	Octagon
9	Nonagon (or enneagon)
10	Decagon

Most people prefer to name a polygon with more than ten sides by the number of sides and the suffix “gon.” For example, a 40 sided polygon would be a “40-gon.”

Two-Dimensional Shape: Triangle

Triangles can be classified by their sides and by their angles.

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Two-Dimensional Shape: Quadrilaterals

The prefix “quad-” means “four”, and “lateral” is derived from the Latin word for “side”. So a quadrilateral is a four-sided polygon. Since it is a polygon, we know it is a two-dimensional figure made of straight sides. A quadrilateral also has four angles formed by its four sides.

 and  are the sides, and  and  are the vertices of the quadrilaterals. 

Line segments  and  joining two non-consecutive vertices are called diagonals.

Two sides like  and  having a common endpoint are called adjacent sides. 

Two-Dimensional Shape: Circle

A circle marks the set of all points at a constant distance from a fixed (centre) point,A,in the same plane. Since the circle has only one centre, you can name the circle by naming its centre. In this way, you can name this circle A.

The distance from the centre point to the circle is called the radius (r). In other words, a line segment joining the centre of a circle with any point on the circle is called a radius (plural: radii) of that circle. AB is a radius of circle A.

The distance from one side of the circle to the other through the centre point is called the diameter (d). In other words, a line segment joining any two points on a circle and passing through the centre of the circle is called a diameter of that circle. The diameter of a circle is twice its radius. PQ is the diameter of circle A.

The perimeter of a circle is called its circumference. The ratio between the circumference and diameter of any circle is π or “pi,” a Greek letter that stands for an irrational number approximately equal to 3.14. Because π is the ratio between the circumference and the diameter, the circle’s circumference is equal to the diameter times π.

C=πd

 Remember this!

• A plane figure has two dimensions. It has length, width but no height. 
• A polygon is a two-dimensional shape bounded by a number of straight lines. It is classified by the number of sides it has. 
• A triangle is a polygon with three sides that can be classified as scalene, isosceles and right based on the length of its sides.
• A triangle can be classified as right, acute and obtuse based on its angles. 
• A quadrilateral is a four-sided polygon. 
• A circle marks the set of all points at a constant distance from a fixed (centre) point.